Projective Dimension, Graph Domination Parameters, and Independence Complex Homology

Details Projective Dimension, Graph Domination Parameters, and Independence Complex Homology Projective Dimension, Graph Domination Parameters, and Independence Complex Homology

2011-10-13

arxiv.org/abs/1110.2841v2

Mathematics

Commutative Algebra

Add references for Chapter 5 and 6. Add remarks 5.7 and 5.8

Scientific paper

We construct several pairwise-incomparable bounds on the projective
dimensions of edge ideals. Our bounds use combinatorial properties of the
associated graphs; in particular we draw heavily from the topic of dominating
sets. Through Hochster's Formula, these bounds recover and strengthen existing
results on the homological connectivity of graph independence complexes.

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